
Due to the symmetry of \(C_3\)  rotation around \(x_0\) , \(\Phi _{K_m, b, B}(\pm x_0) = 0\)  [1]}. Therefore, if \(v_{Dirac}=0\) , then either \(\Phi _{K_m, t, B}(x_0) = 0\)  or \(\Phi _{K_m, t, B}(-x_0) = 0\) . In the former case, both components of \(\Phi _{K_m, B}\)  vanish at \(x_0\) , and therefore Eq. REF  is a normalizable solution if \(v_{Dirac} = 0\) . If the latter is the case, redefine
\(\eta (z) = \frac{\vartheta _{\frac{k \cdot L_1}{2\pi } + \frac{1}{6}, -\frac{1}{6} - \frac{k \cdot (L_2 - L_1)}{2\pi }}\left( \frac{z}{|L_1|} e^{-i \frac{\pi }{6}}, e^{i \frac{2\pi }{3}} \right)}{\vartheta _{\frac{1}{6}, -\frac{1}{6}}\left( \frac{z}{|L_1|} e^{-i \frac{\pi }{6}}, e^{i \frac{2\pi }{3}} \right)} \) 
